FRACTIONS


Adding Fractions with Unlike Denominators

When Fractions have Unlike Denominators, the

Least Common Demonator must first be found.


1

3
+
3

5

To add these fractions, find the least common denominator.

The least common denominator of 3 and 5 is 15.





 1

 3

15 ÷ 3 = 5



 1    x    5    =

 3    x    5    =
5

15


1

3
=
5

15




 3

 5

15 ÷ 5 = 3



 3    x    3    =

 5    x    3    =
9

15


3

5
=
9

15





With like denominators, the fractions can now be added.



1

3
+
3

5



is the same as


5

15
+
9

15
=
14

15

therefore


1

3
+
3

5
=
14

15




If the answer results in an improper fraction, then

change that improper fraction to a mixed number.

2

3
+
1

2
Common Denominator = 6


4

6
+
3

6
=
7

6


7

6
=
1
1

6




If the resulting proper fraction can be reduced, then do so.

1

3
+
4

15
Common Denominator = 15


5

15
+
4

15
=
9

15


9

15
=
3

5




Sometimes both the improper fraction needs to be changed

to a mixed number and the resulting proper fraction needs to

be reduced.

2

3
+
11

15
Common Denominator = 15


10

15
+
11

15
=
21

15


21

15
=
1
6

15


1
6

15
=
1
2

5




RULE

Adding Fractions with Unlike Denominators
Change those Fractions to Fractions with Like Denominators.

Add the Numerators. Keep the Like Denominator.

Change any Improper Fraction to a Mixed Number.

If the Proper Fraction can be Reduced, then do so.